In recent years, two-dimensional NMR has enjoyed wide acceptance. Two-dimensional NMR spectra are easy to analyze. Especially, the interaction between nuclear spins can be elucidated by two-dimensional NMR spectroscopy.
The prior art 2D NMR experiment is now described in detail by referring to FIG. 1, where a pulse sequence with two 90.degree. pulses is used. A general process of measurement by 2D NMR spectroscopy consists of a preparation period preceding the first 90.degree. pulse, an evolution period of t.sub.1, and a detection period of t.sub.2. The preparation period is necessary to maintain the nuclear spin magnetization in its appropriate initial condition. The preparation pulse, or the first 90.degree. pulse, brings the magnetization into nonequilibrium state. This state is caused to evolve in the evolution period t.sub.1. In the detection period t.sub.2 subsequent to the application of the detection period, or the second 90.degree. pulse, the resulting free induction decay signal is detected. The phase and the amplitude of this decay signal reflect the behavior of the magnetization taken in the evolution period t.sub.1. The period t.sub.1 is varied so as to assume n discrete values. The free induction decay signal is detected at each of the n values. As a result, a set of data S (t.sub.1, t.sub.2) is obtained from n free induction decay signals. The obtained data includes information about the behavior of the magnetization in the evolution period t.sub.1, as well as information about the behavior of the magnetization in the detection period t.sub.2. Data about a 2D NMR spectrum .alpha.(.omega..sub.1, .omega..sub.2) is derived by taking the 2D Fourier transform of the data S (t.sub.1, t.sub.2) with respect to t.sub.2 and t.sub.1. FIG. 2 is one example of this 2D NMR spectrum, and in which the spectrum is plotted on the .omega..sub.1 -.omega..sub.2 plane. In 2D NMR spectra, diagonal peaks and cross-peaks appear symmetrically. The relations between the peaks can be known from the symmetrical peaks.
If numerous superimposed peaks appear in a 2D NMR spectrum, it is difficult to understand which of the peaks are coupled to each other. Accordingly, 3D NMR has been proposed which separates the superimposed peaks and permits one to understand them.
FIG. 3 shows a simplest pulse sequence used in 3D NMR spectroscopy. This pulse sequence consists of three 90.degree. pulses. A preparation period, a first evolution period of t.sub.1, a second evolution period of t.sub.2, and a detection period of t.sub.3 are separated by the three pulses.
The first evolution period t.sub.1 is varied so as to take n discrete values. The second evolution period t.sub.2 is changed so as to assume m discrete values. As a result, n.times.m free induction decay signals are produced, and all of them are detected. Thus, a set of data S (t.sub.1, t.sub.2, t.sub.3) is derived from the n.times.m free induction decay signals. The data includes information about the behavior of the magnetization in the period t.sub.3. In addition, the data includes information about the behavior of the magnetization in the periods t.sub.1 and t.sub.3. A three-dimensional NMR spectrum .alpha. (.omega..sub.1, .omega..sub.2, .omega..sub.3) having three frequency parameters .omega..sub.1, .omega..sub.2, .omega..sub.3 is obtained by taking the three-dimensional Fourier transform of the data S (t.sub.1, t.sub.2, t.sub.3) with respect to t.sub.3, t.sub.2, t.sub.1. In this case, .omega..sub.1, .omega..sub.2 and .omega..sub.3 vary in the same domain. However, in one of the most useful 3D experiments as shown in FIG. 9, .omega..sub.1 and .omega..sub.2 vary in the same domain and .omega..sub.3 varies in another domain. 3D experiments developed from homonuclear 2D experiments by adding a dimension of another kind of nucleus belong to this class. Homonuclear 2D spectra are symmetrical and 3D spectra also have this property.
If this 3D NMR spectrum is sliced (.alpha.(.omega..sub.1, .omega..sub.2, .omega..sub.3)) at right angles to the frequency axis .omega..sub.3 at a certain value of .omega..sub.3, for example .omega..sub.3 =.omega..sub.30, then one 2D NMR spectrum is obtained. This 2D NMR spectrum differs greatly in symmetry from 2D NMR spectra obtained by ordinary 2D NMR spectroscopy. In particular, a 2D NMR spectrum obtained by 2D NMR spectroscopy is essentially symmetrical, i.e., .alpha.(.omega..sub.1, .omega..sub.2)=.alpha.(.omega..sub.2, .omega..sub.1). However, this equation does not hold for a 2D NMR spectrum derived by slicing a 3D NMR spectrum.
More specifically, two nuclear spins interact with each other if they are chemically directly coupled to each other or if they are close to each other. As an example, as shown in FIG. 4(a), we now discuss the case in which protons .sup.1 H are spatially close to each other and chemically coupled to .sup.15 N. Let .delta..sub.1, .delta..sub.2, .delta..sub.3, and .delta..sub.4 be the chemical shifts of these four nuclear spins .sup.1 H and .sup.15 N. Since couplings A and B are symmetrical, the corresponding peaks in the 2D NMR spectrum appear symmetrically. However, the chemical shift caused by .sup.1 H differs from .delta..sub.3 and .delta..sub.4. In a 3D NMR spectrum in which these chemical shifts can be distinguished, a pair of symmetrical peaks appear in different sliced planes that are shifted along the frequency axis .omega..sub.3. In each sliced plane, or in each 2D NMR spectrum, the spectrum is asymmetrical. Therefore, in order to search sliced planes for symmetrical peaks, sliced planes or 2D NMR spectra which differ in .omega..sub.3 must be scrutinized one after another. It is very cumbersome and time-consuming to perform this work.
As shown in FIG. 4(b), where carbon nucleus C is coupled to proton .sup.1 H causing chemical shift .delta..sub.1, coupling B has no symmetrical partner. For this reason, in a 3D NMR spectrum, only a peak corresponding to coupling B appears; any peak forming a symmetrical partner does not appear. In this way, information that is useful for making analysis, based on symmetrical peaks in a 3D NMR spectrum, is not contained in those peaks which have no symmetrical partners. Rather, such peaks complicate spectra and can be said to be harmful.